Sixty years ago this month, the February 1957 issue of Popular Science showed the best way to clean a typewriter. Yes, as the picture shows, ultimately, it’s just a matter of dunking it in the kitchen sink with some detergent and letting it soak.
Before you do this, however, you should read the article. It’s important to first strip down the machine of some components, to dry it thoroughly (which might involve placing it in the sun, or even in the warm oven, since you’re in the kitchen anyway), and then properly lubricating as soon as you’re done. The magazine tells you exactly how to do it.